I wasn't sure what the "game theory" was that is being referred to in the OP. Some posts - eg referring to the prisoner's dilemma - have made me wonder whether we're meant to be thinking of game theory in that sense.
If so, before we even start talking about single-play vs iterated, and whether the number of iterations is known in advance or is open-ended, where are the pay-off tables? And what preferences are under analysis - just those that are defined by the logic of play (eg a preference to win combats my PC is part of), or all the preferences that a player brings to the table (eg maybe I have a reason to throw the chess game because that way my opponent will buy me lunch)?
Also: it's certainly possible to reason about payoffs in an open-ended series of iterated plays.
If so, before we even start talking about single-play vs iterated, and whether the number of iterations is known in advance or is open-ended, where are the pay-off tables? And what preferences are under analysis - just those that are defined by the logic of play (eg a preference to win combats my PC is part of), or all the preferences that a player brings to the table (eg maybe I have a reason to throw the chess game because that way my opponent will buy me lunch)?
Also: it's certainly possible to reason about payoffs in an open-ended series of iterated plays.